Why can't I see the render layers in the Scene panel?
The screenshot is showing the Render settings - the icon of a camera. The one next to it (looks like a couple of photos) is the Render Layers icon - click it and you should see the Layers panel.



The tutorial referenced in the question is using an older version of Blender (2.63) where the layout of the properties was different and the Render Layers were included in the Render settings.

Incidentally, the 'Scene' at the top of the panel refers to the current scene - it will change depending on the currently selected scene.